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Two wires A and B are of same material. ...

Two wires A and B are of same material. Their lengths are in the ratio 1:2 and diameters are in the ratio 2:1 when stretched by forces `F_A` and `F_B` respectively they get equal increase in their lengths. Then the ratio `(F_A)/(F_B)` should be

A

`1:2`

B

`1:1`

C

`2:1`

D

`8:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta l= (Fl)/(AY) = (Delta l_(1))/(Delta l_(2))= (F_(A) l_(A))/(d_(A)^(2)) xx (d_(B)^(2))/(F_(B)l_(B))`
`rArr 1= ((F_(A))/(F_(B))) xx ((1)/(2)) ((1)/(2))^(2) rArr (F_(A))/(F_(B)) = 8 :1`
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